{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5d904dee",
   "metadata": {},
   "source": [
    "# Example 1: Function Fitting\n",
    "\n",
    "In this example, we will cover how to leverage grid refinement to maximimze KANs' ability to fit functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94056ef6",
   "metadata": {},
   "source": [
    "intialize model and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0a59179d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directory already exists: ./model\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "seed = 1\n",
    "torch.manual_seed(seed)\n",
    "\n",
    "# initialize KAN with G=3\n",
    "model = KAN(width=[2,1,1], grid=3, k=3, seed=1)\n",
    "\n",
    "# create dataset\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb1f817e",
   "metadata": {},
   "source": [
    "Train KAN (grid=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a87b97b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.46e-02 | test loss: 1.53e-02 | reg: 5.15e+00 : 100%|██| 20/20 [00:04<00:00,  4.78it/s]\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, opt=\"LBFGS\", steps=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52294efd",
   "metadata": {},
   "source": [
    "The loss plateaus. we want a more fine-grained KAN!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3f1cfc9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize a more fine-grained KAN with G=10\n",
    "model = model.refine(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3cc5079",
   "metadata": {},
   "source": [
    "Train KAN (grid=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "898b1794",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 2.93e-04 | test loss: 3.16e-04 | reg: 5.15e+00 : 100%|██| 20/20 [00:04<00:00,  4.92it/s]\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, opt=\"LBFGS\", steps=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcdc0d3d",
   "metadata": {},
   "source": [
    "The loss becomes lower. This is good! Now we can even iteratively making grids finer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a1c25e8a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directory already exists: ./model\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.44e-02 | test loss: 1.51e-02 | reg: 6.29e+00 : 100%|██| 50/50 [00:09<00:00,  5.17it/s]\n",
      "train loss: 2.73e-04 | test loss: 3.15e-04 | reg: 6.31e+00 : 100%|██| 50/50 [00:05<00:00,  8.56it/s]\n",
      "train loss: 1.63e-05 | test loss: 2.15e-05 | reg: 6.31e+00 : 100%|██| 50/50 [00:07<00:00,  6.42it/s]\n",
      "train loss: 1.46e-06 | test loss: 4.63e-06 | reg: 6.31e+00 : 100%|██| 50/50 [00:12<00:00,  3.92it/s]\n",
      "train loss: 1.06e+00 | test loss: 1.63e+00 | reg: 5.62e+00 : 100%|██| 50/50 [00:36<00:00,  1.37it/s]\n"
     ]
    }
   ],
   "source": [
    "grids = np.array([3,10,20,50,100])\n",
    "\n",
    "seed = 2\n",
    "torch.manual_seed(seed)\n",
    "\n",
    "train_losses = []\n",
    "test_losses = []\n",
    "steps = 50\n",
    "k = 3\n",
    "\n",
    "for i in range(grids.shape[0]):\n",
    "    if i == 0:\n",
    "        model = KAN(width=[2,1,1], grid=grids[i], k=k, seed=seed)\n",
    "    if i != 0:\n",
    "        model = model.refine(grids[i])\n",
    "    results = model.fit(dataset, opt=\"LBFGS\", steps=steps)\n",
    "    train_losses += results['train_loss']\n",
    "    test_losses += results['test_loss']\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6be8ba55",
   "metadata": {},
   "source": [
    "Training dynamics of losses display staircase structures (loss suddenly drops after grid refinement)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "156f68a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(train_losses)\n",
    "plt.plot(test_losses)\n",
    "plt.legend(['train', 'test'])\n",
    "plt.ylabel('RMSE')\n",
    "plt.xlabel('step')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ed8d26b",
   "metadata": {},
   "source": [
    "Neural scaling laws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8301085c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'RMSE')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_params = 3 * grids\n",
    "train_vs_G = train_losses[(steps-1)::steps]\n",
    "test_vs_G = test_losses[(steps-1)::steps]\n",
    "plt.plot(n_params, train_vs_G, marker=\"o\")\n",
    "plt.plot(n_params, test_vs_G, marker=\"o\")\n",
    "plt.plot(n_params, 100*n_params**(-4.), ls=\"--\", color=\"black\")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.legend(['train', 'test', r'$N^{-4}$'])\n",
    "plt.xlabel('number of params')\n",
    "plt.ylabel('RMSE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c521e5e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
